Numerical Methods for an Optimal Investment-Consumption Model

This paper examines some numerical techniques for an investment/consumption problem considered by Fleming and Zariphopoulou. The value function v ( x ) satisfies the differential equation of dynamic programming for x > 0. Special monotonicity and concavity features of the problem allow us to prove convergence not only of discrete approximations to v ( x ), but of the corresponding discrete approximations to optimal investment and consumption policies.